306 pages | 17 B/W Illus.
This book is meant as a part of the larger contemporary philosophical project of naturalizing logico-mathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logico-mathematical knowledge in recent research in psychology and cognitive science? The question about this distinctive kind of knowledge is rooted in Plato’s dialogues, and virtually all major philosophers have expressed interest in it. The essays in this collection tackle this important philosophical query from the perspective of the modern sciences of cognition, namely cognitive psychology and neuroscience. Naturalizing Logico-Mathematical Knowledge contributes to consolidating a new, emerging direction in the philosophy of mathematics, which, while keeping the traditional concerns of this sub-discipline in sight, aims to engage with them in a scientifically-informed manner. A subsequent aim is to signal the philosophers’ willingness to enter into a fruitful dialogue with the community of cognitive scientists and psychologists by examining their methods and interpretive strategies.
"In the name of 'cooperative naturalism', Sorin Bangu has put together a first-rate collection of articles by philosophers and psychologists . . . This collection is a welcome addition to the existing literature, and unquestionably succeeds in its main aim of forging connections between the psychology and philosophy of mathematics."—Notre Dame Philosophical Reviews
"Sorin Bangu has assembled an important collection of papers on the project of naturalizing mathematics and logic. It will be a must read both for those who favour that project and also for those who disfavour it."—Jeff Buechner Rutgers University–Newark, USA
1. Introduction. A Naturalist Landscape Sorin Bangu
2. Psychology and the A Priori Sciences Penelope Maddy
3. Reasoning, Rules, and Representation Paul D. Robinson and Richard Samuels
4. Numerical Cognition and Mathematical Knowledge: The Plural Property View Byeong-uk Yi
5. Intuitions, Naturalism, and Benacerraf’s Problem Mark Fedyk
6. Origins of Numerical Knowledge Karen Wynn
7. What Happens When a Child Learns to Count?: The Development of the Number Concept Kristy vanMarle
8. Seeing Numbers as Affordances Max Jones
9. Testimony and Children’s Acquisition of Number Concepts Helen De Cruz
10. Which Came First, the Number or the Numeral? Jean-Charles Pelland
11. Numbers through Numerals: The Role of External Representations Dirk Schlimm
12. Making Sense of Numbers without a Number Sense Karim Zahidi and Erik Myin
13. Beyond Peano: Looking Into the Unnaturalness of Natural Numbers Josephine Relaford-Doyle and Rafael Núñez
14. Beauty and Truth in Mathematics: Evidence from Cognitive Psychology Rolf Reber
15. Mathematical Knowledge, the Analytic Method, and Naturalism Fabio Sterpetti
Recent years have seen a surge of interest in the topics discussed by philosophers of mathematics and physics, particularly those relating to the way in which these disciplines intersect. Titles in this series cover a wide range of exciting and dynamic issues such as category theory, mathematical proofs, computability, emergence, time travel, quantum black holes, and string theory. Authors explore leading questions concerning new directions in the philosophy of mathematics and physics, with the aim of presenting clear, concise, and original monographs for an advanced audience.